Optical Aberrations

and
Aberrometry
 Aberrations
Perfect Eye  would image every infinitesimal
point in a scene to a corresponding infinitesimal
small point on retina

No blurring for each point
Wavefronts are perfectly spherical  emanate
outward, diverge from point


Perfect Eye: converts diverging spherical waves
into converging waves

converging waves must be converge to a

perfectly spherical point on retina
 Perfect imaging Never occurs 
at periphery

- diffraction - interaction with pupil

margin

Aberration = Deviation of changing

wave fronts from perfect sphere
Monochromatic Aberrations
Aberrations for a specific wavelength of
visible light
Classifications:
- Spherical refractive error (defocus)
 Cylindrical refractive error (astigmatism)
 Spherical aberration
 Coma
 Higher-order aberrations
 Chromatic Aberrations
 Depends upon the color or light
wavelength
 Causes:- light dispersion in the cornea,
aqueous, crystalline lens and vitreous
-Variation index of refraction
 Refractive surgery techniques CANNOT
correct chromatic aberrations
 Spectral sensitivity of the eye helps to
reduce the effects of chromatic aberration
Yesterday! optical imperfection
and aberrations Only theory

No clinical practice

Today!  laser refractive surgery

 potential for correction

Needs knowledge
 Measurement of Optical
Quality
-By three common methods
Method I : - Description of detailed shape of the image
for a simple geometrical object e.g. a point or line of
light
 PSF (point spread function): distribution of light in the
image plane for a point
 LSF (line spread function): distribution for a line
object
 Blurring effects: blur circle diameter (width of image)
 Strehl ratio (height)
 Method II
 Description of the loss of contrast in image
of a sinusoidal grating object
 Sinusoidal grating objects  aberrations of
the imaging system remains the same over
the full extent of the object i.e. “preservation
form”
 Ratio of image contrast to object contrast 
blurring effect of optical imperfections

 Variation of this ratio with spatial frequency
 Modulation transfer function (MTF)
 Methods II… cont..

-Difference between spatial phase of image and phase

of the object + variation with spatial frequency and
orientation of the grating

Phase transfer function (PTF)
-MTF + PTF  Optical transfer function (OTF)
Fourier Transform:
-Mathematical linkage of PSF, LSF, MTF, PTF, OTF
-Computing the retinal image (naturally inaccessible)
for any visual object
 Method III

 Specifying optical quality in terms of optical

aberrations
 Description: Ray aberrations (deviation of light
rays from perfect reference ray)
 Wave front aberrations (deviation of optical wave
fronts from ideal wave front)
 Aberrometry: description of optical imperfections
of the eye
 All secondary measures of optical quality
(PSF,LSF,MTF,PTF, and OTF) may be derived
 Useful approach for customized corneal ablation
 Definition and Interpretation
of Aberration Maps
Optical Path Length (OPL):
number of times a light wave must oscillate in
traveling from one point to another
- product of physical path length with refractive index
Optical Path Difference (OPD):
- comparing the OPL for a ray passing in the plane of
exit pupil with the chief ray passing through pupil
center
- optical aberrations are differences in optical path
difference
 Causes of Aberrations
 Thickness anomalies of the tear film,
cornea, lens, anterior chamber, post
chamber
 Anomalies of refractive index in ocular
media due to aging, inflammation, etc.
 Decentering or tilting the various optical
components of the eye
 Optimum retinal image  same optical
distance for all object point
 Wavefront aberration map  shows
extent of violated ideal condition

Reversing the direction of light

propagation
Map of OPD across the pupil plane 
shape of aberrated wave front
 History of Measuring Aberration
Maps
Scheiner (1619)  Scheiner’s disk with 2 pinholes
single distant point of light  optically imperfect eye
 2 retinal image
Porterfield (1747)  used Scheiner disk to measure
refractive error
Smirnov  used Scheiner method  central fixed and
moveable light source for outer pinhole

Adjusting outer source horizontal or vertical

Redirect outer light  patient reports seeing single point
 Hartmann method  numerous holes in opaque
screen  each hole aperture for a narrow ray bundle

Tracing errors in direction of propagation

Error in wavefront slope
Shack & Platt  an array of tiny lenses focusing into
an array of small spots

Measuring displacement for each spot from lenslet
axis

Shape of aberrated wavefront
(Shack-Hartmann)
 Liang (1994): Used Shack-Hartmann
Wavefront sensor for Human Eye

2 relay lenses focusing lenslet array

onto the entrance pupil

Subdividing the reflected wavefront

immediately as it emerges from the eye

Spot images formed  capture by a

video sensor  computer analysis
 Taxonomy of Optical
Aberrations
• Transverse ray aberration (slope):
Angle (t) between aberrated ray and the
non- aberrated reference ray
• Longitudinal ray aberration:
focusing error = 1/z (diopters) =
transverse aberration/ ray height at pupil
plane
 If aberration is defocus  Longitudinal
aberration is constant = spherical refractive
error
 Coma or spherical aberration  longitudinal
aberration varies with pupil location
 Rate of slope of wavefront (i.e: local
curvature)
in horizontal and vertical directions

Laplacian map of the aberration ( in diopters)
 PSF and Strehl’s Ratio
 PSF = Squared magnitude of Fourier transform
 Strehl’s Ratio = actual intensity in the center of spot
maximum intensity of a diffraction – limited spot
Pupil diameter intensity of a diffraction – limited –
spot
PSF have multiple peaks  2 or more point images
for single point

Di- or polyplopia
Pupil diameter  excludes most of aberrations
Much improved image quality 
clearer more focused retinal image
Zernike Polynomials

Wavefront shape representation in

polar coordinates (r/q)
r = radial distance from pupil center
q = angle of the semi meridian for a
given point on the wavefront
 Ordering of Aberrations
Wavefront (difference in shape between
the aberrated wave front from ideal
wave front ) for myopia, hyperopia and
astigmatism  second order
 Coma is third order aberration =
wavefront error is well fit with third
order polynomial
 Spherical aberration is fourth order
aberration.
 Corneal Topography Vs.
Wavefront
Topography:
- Utilizes information from the corneal
surface
- Two – dimensional mapping profile of
keratometry
Wavefront measurement device:
- Two dimensional profile of refractive error
- Used to attempt to smooth corneal points
on the retinal fovea
 Principles of Wavefront
Measurement Devices
Three Different principles by which,
wavefront aberration is collected and
measured:
1- Outgoing Reflection Aberrometry
(Shack – Hartmann)
2- Retinal lmaging aberrometry
(Tscherning and Ray Tracing)
3- Ingoing Adjustable Refractometry
(Spatially Resolved Refractometer)
 Outgoing Reflection Aberrometry
(Shack – Hartmann)
In 1994:Liang and Bill used Shack- Hartmann
principle
In 1996: Adaptive optics as defined by Shack-
Hartmann sensor use to view cone photoreceptors
 Shack- Hartmann wavefront sensor utilizes >100
spots, created by (> 100) lenslets
 The aberrated light exiting the eye  CCD
detection
Distance of displaced (dx) focused spot from
ideal  shows aberration.
Outgoing Reflection aberrometry …
(cont.)

Limitation:
Multiple scattering from choroidal
structures, interference echo
 insignificant in comparison to
axial
length
 Retinal Imaging Aberrometry
(Tscherning and Ray Tracing)

In 1997:Howland & Howland used Tscherning

aberroscope design together with a
cross cylinder
Seilor: used a spherical lens to project a 1mm
grid pattern onto the retina

Para- axial aperture system  visualization
and photography of aberrated pattern
 Tscherning and Ray Tracing
(cont.)
Limitation:
-This wave front sensing used an idealized eye
model (Gullstrand)
-The eye model is modified according to patient’s
refractive error
Tracey Retinal ray tracing: slightly different
- Uses a sequential projection of spots onto the
retina
- Captured and traced to find wavefront pattern
- 64 sequential retinal spots can be traced in 12
ms
 Ingoing Adjustable Refractometry
(Spatially Resolved Refractometer)
 In 1961: - Smirnov used scheiner principle 
subjective adjustable refractometry
 Peripheral beams of incoming light are subjectively
redirected to a central target to cancel ocular
aberrations
 In 1998: Webb and Bums used spatially Resolved
refractometer (SRR)
 37 testing spots are manually directed to overlap the
central target
 Limitation: - Lengthy time for subjective alignment
 Ingoing adjustable
Refractometry …(cont.)

Objective variant:
 Slit retinoscopy  rapid scanning
along specific axis and orientation
 Capture of fundus reflection 
wavefront aberration
 Commercial Wavefront
Devices
Outgoing Reflection Retinal lmaging Ingoing adjustable
Abberrometry Abberrometry Refractometry
Shack-Hartmann principles Tscherring principle Scheiner principles

Alcon summit/ Autonomous wave light wavefront Emory vision SRR

analyzer Nidek OPD scan
Custom cornea meas.device Schwind wavefront (slit skioloscopy)
analyzer
VisX 20/10 perfect vision Tracey retinal ray
wavescan tracing
Bausch & Lomb zyoptics
Aesculap Medical WOSCA
Careful comparison of various
wavefront measuring principles
and their specific devices has
not yet been performed
clinically